curves fotoelectric effect

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Project PHYSNET Physics Bldg. Michigan State University East Lansing, MI

MISN-0-213

THE PHOTOELECTRIC EFFECT

l ight off requency ,

intensity

n

I

galvanometer

variable voltage V

platecol lector

1

THE PHOTOELECTRIC EFFECT

by

M. Brandl

1. Overviewa. Macroscopic View of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1b. Microscopic View of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1c. Photoemission Supports the Photon Model . . . . . . . . . . . . . . 1

2. The Experimental Evidencea . F i r s t O b s e r v a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1b. Millikans Photoelectric Experiment . . . . . . . . . . . . . . . . . . . . . 2c. Results of Millikans Experiment . . . . . . . . . . . . . . . . . . . . . . . . .3d. Dependence on Intensity of Incident Light ...............4e. Dependence on Frequency of Incident Light . . . . . . . . . . . . . . 5f. Time Dependence of Photoemission . . . . . . . . . . . . . . . . . . . . . . 6

3. The Classical Interpretationa. Description of the Mechanism .. . . . . . . . . . . . . . . . . . . . . . . . . . 6b. Dependence on Intensity of Incident Light ...............6c. Dependence on Frequency of Incident Light . . . . . . . . . . . . . . 7d. Time Dependence of Photoemission ..................... 7e. Failure of the Electromagnetic Wave Model . . . . . . . . . . . . . . 7

4. The Photon Modela. Plancks Quantum Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 8b. Einsteins Photon Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8c. Macroscopic Beams Contain Many Photons . . . . . . . . . . . . . . 8d. Microscopic Systems Interact with Photons . . . . . . . . . . . . . . 9

5. The Photon Interpretationa. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9b. Einsteins Photoelectric Equation ........................9c. Dependence on Intensity of Incident Light . . . . . . . . . . . . . . 10d. Dependence on Frequency of Incident Light . . . . . . . . . . . . 10e. Time Dependence of Photoemission . . . . . . . . . . . . . . . . . . . . 11f. Success of the Photon Interpretation . . . . . . . . . . . . . . . . . . . . 11

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1

A. Explanation of the Work Function . . . . . . . . . . . . . . . . . . . . 1 2

B. Time Delay for Classical Photoemission . . . . . . . . . . . 13


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MISN-0-213 15

number density of atoms is, therefore,

Na =1

d3. (10)

The number density of atoms can also be determined from the mass den-sity of the metal and the mass of each atom:

Na =

. (11)

Combining the two expressions and solving for d gives

d = 1/3

. (12)

Finally, we can determine how long it should take for photoemission tooccur. The time tem required for emission to occur is just the amount oftime needed for the electron to absorb an amount of energy equal to theamount by which it is bound to the metal, . The first electrons emittedwill be the ones with the smallest binding energy, that being equal to thework function of the metal, 0. Therefore, we can find the minimum valueof tem by setting EL,max = 0 in Eq. (11) and solving for t, which gives

tem =0Id2

. (13)

Combining Eqs. (12) and (13), the time delay is

tem =0I

2/3. (14)

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MISN-0-213 PS-1

PROBLEM SUPPLEMENT

h = 6.62559 1034 J s = 4.13557 1015 eV s

J = 6.24181 1018 eV

c = 3.00 108 m/s

1. The longest wavelength of light that will cause photoemission fromsodium is approximately 540 nm.

a. Find the work function of sodium.

b. Find the maximum kinetic energy for photoelectrons emitted whenlight of wavelength 400 nm strikes a sodium plate.

2. Pure silver has a work function of 0 = 4.7 eV. A crude calculationof the type used in the text, using the atomic weight and densityof silver, gives a spacing between atoms in a silver crystal of aboutd = 12 nm. Note that d-cubed was taken to be the mass-per-atomdivided by the density of the silver. It has been found that light ofintensity 1 1010 W/m2 can still cause photoemission from silver. If

the electromagnetic wave interpretation were correct, how long wouldit take before the first photoelectrons were emitted?

3. When light of wavelength 244 nm illuminates an aluminum surface, astopping potential of 1.0 V is needed to reduce the photoelectric currentto zero.

a. Find the work function of aluminum.

b. Find the wavelength of light that would require a stopping potentialof 1.5V.

Brief Answers:

1. a. 0 = 2.3eV.

b. KE,max = 0.8eV.

2. tem = 5.23 107 s = 1.66 years

3. a. 0 = 4.08eV

b. = 222nm.

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MISN-0-213 ME-1

MODEL EXAM

h = 6.62559 1034 J s = 4.13557 1015 eV s

J = 6.24181 1018 eV

c = 3.00 108 m/s

1. See Output Skills K1-K4 in this modules ID Sheet.

2. The photoelectric work function of aluminum is 0 = 4.08eV.a. Find the cutoff frequency and the corresponding cutoff wavelength

for photoemission from aluminum.

b. Find the maximum photoelectron kinetic energy and the stoppingpotential when (ultraviolet) light of wavelength 200 nm illuminatesan aluminum plate.

3. Photoemission can occur in a gas, as well as in a metal. Consider the(extremely hypothetical) case of a monatomic hydrogen gas with all ofthe atoms being in their ground state. Each electron is bound to itscorresponding nucleus by an amount equal to 13.6 eV. Since the radiusof an electrons orbit in a hydrogen atom is r = 0.053 nm, each electroncan absorb only that amount of energy from a beam of light that fallson a disc whose area is r2 = 8.82 1021 m2. If light of intensityI= 1.00 W/m2 illuminates the gas, find how long the electromagneticwave theory would predict it should take for photoemission to occur.

Brief Answers:

1. See this modules text.

2. a. 0 = 9.87 1014/s, 0 = 304.1 nm

b. Ek,max = 2.12eV, V0 = 2.12 V

3. tem = 247 s.

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curves fotoelectric effect

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